74.13.18 problem 35

Internal problem ID [16384]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number : 35
Date solved : Tuesday, January 28, 2025 at 09:07:23 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(t),t$5)+3*diff(y(t),t$4)+3*diff(y(t),t$3)+diff(y(t),t$2)=0,y(t), singsol=all)
 

\[ y = \left (t^{2} c_5 +t c_4 +c_{3} \right ) {\mathrm e}^{-t}+c_{2} t +c_{1} \]

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 48

DSolve[D[ y[t],{t,5}]+3*D[y[t],{t,4}]+3*D[ y[t],{t,3}]+D[y[t],{t,2}]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _1^t\int _1^{K[2]}e^{-K[1]} (c_1+K[1] (c_2+c_3 K[1]))dK[1]dK[2]+c_5 t+c_4 \]